Russell's strange opinions

[WM]

An existent class is a class having at least one member. [p. 47]

And whether, in particular, Zermelo's axiom is true or false is a question which, while more fundamental matters are in doubt, is very likely to remain unanswered. [p. 53]

[B. Russell: "On some difficulties in the theory of transfinite numbers and order types", Proc. London Math. Soc. (2) 4 (1907)]

Regards, WM

[Timothy Golden]

Maybe he was on a bender when he wrote his Principia Mathematica. The notational issues from the outset are extraordinarily bad.

Much as he weighs in on types in mathematics he as quickly backs away from it right in the introduction.
Somewhat this effect goes on to this day.
The char type in C is 8 bits long.
The short type is 16 bits.
The int type...
Whatever, aren't these all the same things in differing sizes?
So dismiss type theory? Set theory isn't far off.
Other serious issues accrue in the hardware such as endian-ness in the universal translation of binary code. I'm afraid that as the data routes loop around that the programmer is merely corrective since digging through the literature means less than seeing it experimentally. Throw into your code the ntohs() and htons() routines. They may do nothing but supposedly your code is now portable, fingers crossed that they didn't cross their fingers on the other side.
Byte alignment and structure packing are more the things that make the machine tick cleanly.

For mathematicians their numbers are sizeless but not typeless. Still we see types such as rational values and irrational values introduced into the same domain; one abiding by epsilon-delta, the other having no such need... and are we still buying that?
I've evolved tremendously on this recently, and the realization that they had no compiler telling them they were wrong; indeed they were the compilers. They were wrong.

[Mostowski Collapse]

The strange thing is rather that WM expresses his psychosis
in a few lines, and not in a large blob of nonsense citations.

[FromTheRafters]

He's probably exhausted and depleted from manipulating proper subsets
of natural numbers late into the night. Some always seem to get away
from him. We're sorry for his loss, but we warned him about those
rubber sets developing leaks.

Mostowski Collapse expressed precisely :

[Mostowski Collapse]

WM has obviously extended his witch hunt, from
those that support the axiom of infinity, to

those that are agnostic of the axiom of infinity,
his relegious war now spans more enemies.

[Mostowski Collapse]

Also "existent" is derived from having a non empty "extend".
And is a definition inside Russells Paper, and doesn't
say the same as "existing". Its a simple explanation

of what this sentence here means, where A is a class:

EXIST(x):A(x)

It means A has a least one member. Or as Russell
put it in the footnote and to have a simpler phrasing
that EXIST(x):A(x), he says A is an existent class.

See for yourself:
https://fa.ewi.tudelft.nl/~hart/37/onderwijs/set_theory/material/russell-some-difficulties.pdf

I guess he uses it when explaining the axiom of choice,
could be even a word that is needed to get a more
verbatim translation of Zermelo.

[Mostowski Collapse]

The word "existent" seems to be quite Russellian, its not
needed to translate Zermelo. Zermelo rather has a word
for the opposite and more for sets than for classes,

i.e. when a set is empty, he uses the word:

"verschwindet"
https://context.reverso.net/translation/german-english/verschwindet

"existent" would then mean "nicht verschwindet". The problem
with translating "verschwindet", it would translate into verb
"disappear", suggesting that sets are non-rigid modal

placeholders. Although the german language is like that,
and WM causes constantly problems because of that, Zermelo
uses "disappear" adjektively, characterising the

result of an operation.

See for yourself:
Zermelo 1908
https://zenodo.org/record/1428264/files/article.pdf

Because Zermelo characterizes the outcome of operations
on sets, which give an again sets, his axiom of choice is
also not some global choice. Russells dealing with classes

has the danger that one arrives at a different axiom of
choice, than that promoted by Zermelo.

[zelos...@gmail.com]

is this all you got these days? taking quotes from long since dead people?

[Mostowski Collapse]

Quite in line with:

Such results show that axiomatic Set Theory is hopelessly
incomplete. . . If there are a multitude of set theories
then none of them can claim the central place in
Mathematics. (Mostowski-1967)

Beyond classical analysis there is an infinity of different
mathematics and for the time being no definitive
reason compels us to chose one rather than another.
(Dieudonné-1976)

SOME SET THEORIES ARE MORE EQUAL
MENACHEM MAGIDOR
http://logic.harvard.edu/EFI_Magidor.pdf

WM schrieb am Sonntag, 28. November 2021 um 11:47:52 UTC+1: